Computation of many-particle quantum trajectories with exchange interaction: Application to the simulation of nanoelectronic devices

TL;DR

This paper introduces an algorithm for simulating many-particle quantum trajectories with exchange interaction, applicable to fermions and bosons, ensuring exchange symmetry and enabling realistic nanoelectronic device modeling.

Contribution

It presents a universal algorithm based on conditional Bohmian wave functions that directly enforces exchange symmetry without relying on exchange-correlation functionals.

Findings

Algorithm accurately reproduces exchange symmetry in quantum trajectories.

Numerical tests confirm viability for electron transport simulations.

Successfully models current and fluctuations in nanoelectronic devices.

Abstract

Following Ref. [Oriols X 2007 Phys. Rev. Lett., 98 066803], an algorithm to deal with the exchange interaction in non-separable quantum systems is presented. The algorithm can be applied to fermions or bosons and, by construction, it exactly ensures that any observable is totally independent from the interchange of particles. It is based on the use of conditional Bohmian wave functions which are solutions of single-particle pseudo-Schr\"odinger equations. The exchange symmetry is directly defined by demanding symmetry properties of the quantum trajectories in the configuration space with a universal algorithm, rather than through a particular exchange-correlation functional introduced into the single-particle pseudo-Schr\"odinger equation. It requires the computation of N^2 conditional wave functions to deal with N identical particles. For separable Hamiltonians, the algorithm reduces to the standard Slater determinant for fermions, or permanent for bosons. A numerical test for a two-particle system, where exact solutions for non-separable Hamiltonians are computationally accessible, is presented. The numerical viability of the algorithm for quantum electron transport (in a far-from equilibrium time-dependent open system) is demonstrated by computing the current and fluctuations in a nano-resistor, with exchange and Coulomb interactions among electrons.